a) is it possible to have an electric bicycle that charges with a balance charger but also has a BMS in the battery pack?
Is it not possible to regulate the BMS Not to balance the cells while charging the battery, but only balance the cells while the battery is not connected to a charger?
Those are two separate questions, so:
First, you can always choose to add a separate balance connector for your battery, wired to the cells just like the balance/sense connector from your BMS. Then you also add a separate main +/- from the block of cells (spearate from the ones to the BMS). Then use those for the external balance charger, per that charger's instructions.
Second, if you have a smart BMS (like the various bluetooth types), it may have an option in the app to turn on or off the balancing function manually. Whether this will allow balancing when not charging depends on the settings available in the app, and how the balancers work in the BMS.
There are two types of balancers:
The most common is passive resistive "shunts" that simply drain down high cells above some setpoint, until they reach a second setpoint. Any cell below those points will not be altered, so if it's lower than the others it will remain so, if no charging current is flowing to continue filling it up.
Active charge-shuffling is becoming more common, and this can operate at any time, moving charge from high cells to low cells, depending on the setpoints provided.
You'd need to buy the BMS with the type of balancing you want, and the type and amount of control over it you want.
There are also BMS that do not have balancers at all, but only protection circuitry. (these are often used in cheap battery packs, which is one reason the cheaper the pack is, the worse it tends to perform, becuase it's alreayd made of cells that wont' stay balanced because they're very different from each other, and wihtout something to help rebalance them they get worse and worse on every usage cycle).
b) is there any difference between a
i) pulse
and a
ii) balance
charger?
Without a link to one to show us what you mean by "pulse charger", the only thing I can think of that could be described as that would be a desulfation device for lead-acid, which uses pulses of higher voltage to attempt to remove the crystals that form in lead-acid batteries that short out the plates.
If that's what the pulse charger you are thinking of does, then it is very different from a balance charger, and is not meant to be used on lithium packs.